It is known to “bond” multiple communication channels together to provide increased data bandwidth. For example, ISDN supports aggregating data in multiple “B” (bearer) channels into a composite stream. Likewise, h.320 videoconferencing coordinates multiple ISDN channels.
Similarly, it is known to aggregate bandwidth in multiple channels within an IEEE-802.11g (called “super-g” or “turbo-g”, for nominal 108 or 125 megabits per second communications, instead of the normal peak 54 megabits per second available for a single channel), or 802.11n or 802.11ac communication for even higher data rates.
An issue arises when communicating multiple modulated data streams through a common amplifier. Each modulated signal has a peak to average power ratio. The lower the ratio, the more efficiently the power amplifier of the transmitter can operate, and, given legal or practical limits on maximum transmit power, the greater the communication range or bandwidth. When multiple streams are combined, it is possible for the peak signal to double, leading to a requirement for an amplifier having double the peak power, or limiting the power of each component to less than the normal maximum. Therefore, significant inefficiencies may arise when multiple modulated signals are merely summed before the power amplifier, and seeking to sum after the power amplifier also creates problems.
On the other hand, if instead of the multiple modulated signals, a single data stream is provided, backwards compatibility of the system with normal users of the communication channel might be impaired.
Therefore, from a transmit perspective, it is difficult to increase the effective bandwidth of a system by bonding two wireless channels having legacy protocol together, while maintaining efficiency and backwards compatibility.
A common signal format for mobile wireless communications is orthogonal frequency-domain multiplexing, or OFDM, and closely related formats such as orthogonal frequency-domain multiple access (OFDMA). For a signal conveyed on an OFDM channel, this is characterized in the frequency domain by a bundle of narrow adjacent subchannels, and in the time domain by a relatively slow series of OFDM symbols each with a time T, each separated by a guard interval ΔT (see FIG. 1). Within the guard interval before each symbol is a cyclic prefix (CP), comprised of the same signal in the symbol period, cyclically shifted in time. This CP is designed to reduce the sensitivity of the received signal to precise time synchronization in the presence of multipath, i.e., radio-frequency signals reflecting from large objects in the terrain such as tall buildings, hills, etc. If a given symbol is received with a slight time delay (less than ΔT), it will still be received without error. In addition to the data symbols associated with the OFDM “payload”, there is also typically a “preamble” signal that establishes timing and other standards. The preamble may have its own CP, not shown in FIG. 1.
In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated and inter-sub-carrier guard bands are not required. This greatly simplifies the design of both the transmitter and the receiver; unlike conventional FDM, a separate filter for each sub-channel is not required. The orthogonality requires that the sub-carrier spacing is Δf=k/(TU) Hertz, where TU seconds is the useful symbol duration (the receiver side window size), and k is a positive integer, typically equal to 1. Therefore, with N sub-carriers, the total passband bandwidth will be B≈N·Δf (Hz). The orthogonality also allows high spectral efficiency, with a total symbol rate near the Nyquist rate. Almost the whole available frequency band can be utilized. OFDM generally has a nearly “white” spectrum, giving it benign electromagnetic interference properties with respect to other co-channel users.
When two OFDM signals are combined, the result is in general a non-orthogonal signal. While a receiver limited to the band of a single OFDM signal would be generally unaffected by the out-of-channel signals, when such signals pass through a common power amplifier, there is an interaction, due to the inherent nonlinearities of the analog system components.
OFDM requires very accurate frequency synchronization between the receiver and the transmitter; with frequency deviation the sub-carriers will no longer be orthogonal, causing inter-carrier interference (ICI), i.e. cross-talk between the sub-carriers. Frequency offsets are typically caused by mismatched transmitter and receiver oscillators, or by Doppler shift due to movement. While Doppler shift alone may be compensated for by the receiver, the situation is worsened when combined with multipath, as reflections will appear at various frequency offsets, which is much harder to correct.
The orthogonality allows for efficient modulator and demodulator implementation using the fast Fourier transform (FFT) algorithm on the receiver side, and inverse FFT (IFFT) on the sender side. While the FFT algorithm is relatively efficient, it has modest computational complexity which may be a limiting factor.
One key principle of OFDM is that since low symbol rate modulation schemes (i.e. where the symbols are relatively long compared to the channel time characteristics) suffer less from intersymbol interference caused by multipath propagation, it is advantageous to transmit a number of low-rate streams in parallel instead of a single high-rate stream. Since the duration of each symbol is long, it is feasible to insert a guard interval between the OFDM symbols, thus eliminating the intersymbol interference. The guard interval also eliminates the need for a pulse-shaping filter, and it reduces the sensitivity to time synchronization problems.
The cyclic prefix, which is transmitted during the guard interval, consists of the end of the OFDM symbol copied into the guard interval, and the guard interval is transmitted followed by the OFDM symbol. The reason that the guard interval consists of a copy of the end of the OFDM symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of the multipaths when it performs OFDM demodulation with the FFT.
The effects of frequency-selective channel conditions, for example fading caused by multipath propagation, can be considered as constant (flat) over an OFDM sub-channel if the sub-channel is sufficiently narrow-banded, i.e. if the number of sub-channels is sufficiently large. This makes equalization far simpler at the receiver in OFDM in comparison to conventional single-carrier modulation. The equalizer only has to multiply each detected sub-carrier (each Fourier coefficient) by a constant complex number, or a rarely changed value. Therefore, receivers are generally tolerant of such modifications of the signal, without requiring that explicit information be transmitted.
OFDM is invariably used in conjunction with channel coding (forward error correction), and almost always uses frequency and/or time interleaving. Frequency (subcarrier) interleaving increases resistance to frequency-selective channel conditions such as fading. For example, when a part of the channel bandwidth is faded, frequency interleaving ensures that the bit errors that would result from those subcarriers in the faded part of the bandwidth are spread out in the bit-stream rather than being concentrated. Similarly, time interleaving ensures that bits that are originally close together in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would happen when travelling at high speed. Therefore, similarly to equalization per se, a receiver is typically tolerant to some degree of modifications of this type, without increasing the resulting error rate.
The OFDM signal is generated from the digital baseband data by an inverse (fast) Fourier transform (IFFT), which is computationally complex, and as will be discussed below, generates a resulting signal having a relatively high peak to average power ratio (PAPR) for a set including a full range of symbols. This high PAPR, in turn generally leads to increased acquisition costs and operating costs for the power amplifier (PA), and typically a larger non-linear distortion as compared to systems designed for signals having a lower PAPR. This non-linearity leads, among other things, to clipping distortion and intermodulation (IM) distortion, which have the effect of dissipating power, causing out of band interference, and possibly causing in-band interference with a corresponding increase in bit error rate (BER) at a receiver.
In a traditional type OFDM transmitter, a signal generator performs error correction encoding, interleaving, and symbol mapping on an input information bit sequence to produce transmission symbols. The transmission symbols are subjected to serial-to-parallel conversion at the serial-to-parallel (S/P) converter and converted into multiple parallel signal sequences. The S/P converted signal is subjected to inverse fast Fourier transform at IFFF unit. The signal is further subjected to parallel-to-serial conversion at the parallel-to-serial (P/S) converter, and converted into a signal sequence. Then, guard intervals are added by the guard interval (GI) adding unit. The formatted signal is then up-converted to a radio frequency, amplified at the power amplifier, and finally transmitted as an OFDM signal by a radio antenna.
On the other hand, in a traditional type of the OFDM receiver, the radio frequency signal is down-converted to baseband or an intermediate frequency, and the guard interval is removed from the received signal at the guard interval removing unit. Then, the received signal is subjected to serial-to-parallel conversion at S/P converter, fast Fourier transform at the fast Fourier transform (FFT) unit, and parallel-to-serial conversion at P/S converter. Then, the decoded bit sequence is output.
It is conventional for each OFDM channel to have its own transmit chain, ending in a power amplifier (PA) and an antenna element. However, in some cases, one may wish to transmit two or more separate OFDM channels using the same PA and antenna, as shown in FIG. 2. This may permit a system with additional communications bandwidth on a limited number of base-station towers. Given the drive for both additional users and additional data rate, this is highly desirable. The two channels may be combined at an intermediate frequency using a two-stage up-conversion process as shown in FIG. 2. Although amplification of real baseband signals is shown in FIG. 2, in general one has complex two-phase signals with in-phase and quadrature up-conversion (not shown). FIG. 2 also does not show the boundary between digital and analog signals. The baseband signals are normally digital, while the RF transmit signal is normally analog, with digital-to-analog conversion somewhere between these stages.
Consider two similar channels, each with average power P0 and maximum instantaneous power P1. This corresponds to a peak-to-average power ratio PAPR=P1/P0, usually expressed in dB as PAPR[dB]=10 log(P1/P0). For the combined signal, the average power is 2 P0 (an increase of 3 dB), but the maximum instantaneous power can be as high as 4 P1, an increase of 6 dB. Thus, PAPR for the combined signal can increase by as much as 3 dB. This maximum power will occur if the signals from the two channels happen to have peaks which are in phase. This may be a rare transient occurrence, but in general the linear dynamic range of all transmit components must be designed for this possibility. Nonlinearities will create intermodulation products, which will degrade the signal and cause it to spread into undesirable regions of the spectrum. This, in turn, may require filtering, and in any case will likely reduce the power efficiency of the system.
Components with required increases in linear dynamic range to handle this higher PAPR include digital-to-analog converters, for example, which must have a larger number of effective bits to handle a larger dynamic range. But even more important is the power amplifier (PA), since the PA is generally the largest and most power-intensive component in the transmitter. While it is sometimes possible to maintain components with extra dynamic range that is used only a small fraction of the time, this is wasteful and inefficient, and to be avoided where possible. An amplifier with a larger dynamic range typically costs more than one with a lower dynamic range, and often has a higher quiescent current drain and lower efficiency for comparable inputs and outputs.
This problem of the peak-to-average power ratio (PAPR) is a well-known general problem in OFDM and related waveforms, since they are constructed of multiple closely-spaced subchannels. There are a number of classic strategies to reducing the PAPR, which are addressed in such review articles as “Directions and Recent Advances in PAPR Reduction Methods”, Hanna Bogucka, Proc. 2006 IEEE International Symposium on Signal Processing and Information Technology, pp. 821-827, incorporated herein by reference. These PAPR reduction strategies include amplitude clipping and filtering, coding, tone reservation, tone injection, active constellation extension, and multiple signal representation techniques such as partial transmit sequence (PTS), selective mapping (SLM), and interleaving. These techniques can achieve significant PAPR reduction, but at the expense of transmit signal power increase, bit error rate (BER) increase, data rate loss, increase in computational complexity, and so on. Further, many of these techniques require the transmission of additional side-information (about the signal transformation) together with the signal itself, in order that the received signal be properly decoded. Such side-information reduces the generality of the technique, particularly for a technology where one would like simple mobile receivers to receive signals from a variety of base-station transmitters. To the extent compatible, the techniques disclosed in Bogucka, and otherwise known in the art, can be used in conjunction with the techniques discussed herein-below.
Various efforts to solve the PAPR (Peak to Average Power Ratio) issue in an OFDM transmission scheme, include a frequency domain interleaving method, a clipping filtering method (See, for example, X. Li and L. J. Cimini, “Effects of Clipping and Filtering on the Performance of OFDM”, IEEE Commun. Lett., Vol. 2, No. 5, pp. 131-133, May, 1998), a partial transmit sequence (PTS) method (See, for example, L. J Cimini and N. R. Sollenberger, “Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences”, IEEE Commun. Lett., Vol. 4, No. 3, pp. 86-88, March, 2000), and a cyclic shift sequence (CSS) method (See, for example, G. Hill and M. Faulkner, “Cyclic Shifting and Time Inversion of Partial Transmit Sequences to Reduce the Peak-to-Average Ratio in OFDM”, PIMRC 2000, Vol. 2, pp. 1256-1259, September 2000). In addition, to improve the receiving characteristic in OFDM transmission when a non-linear transmission amplifier is used, a PTS method using a minimum clipping power loss scheme (MCPLS) is proposed to minimize the power loss clipped by a transmission amplifier (See, for example, Xia Lei, Youxi Tang, Shaoqian Li, “A Minimum Clipping Power Loss Scheme for Mitigating the Clipping Noise in OFDM”, GLOBECOM 2003, IEEE, Vol. 1, pp. 6-9, December 2003). The MCPLS is also applicable to a cyclic shifting sequence (CSS) method.
In a partial transmit sequence (PTS) scheme, an appropriate set of phase rotation values determined for the respective subcarriers in advance is selected from multiple sets, and the selected set of phase rotations is used to rotate the phase of each of the subcarriers before signal modulation in order to reduce the peak to average power ratio (See, for example, S. H. Muller and J. B. Huber, “A Novel Peak Power Reduction Scheme for OFDM”, Proc. of PIMRC '97, pp. 1090-1094, 1997; and G. R. Hill, Faulkner, and J. Singh, “Deducing the Peak-to-Average Power Ratio in OFDM by Cyclically Shifting Partial Transmit Sequences”, Electronics Letters, Vol. 36, No. 6, 16th March, 2000).
What is needed is a practical method and associated apparatus for reducing the PAPR of combined OFDM signals, in a way that does not degrade the received signal or require the transmission of side-information.
The following patents, each of which are expressly incorporated herein by reference, relate to peak power ratio considerations: U.S. Pat. Nos. 7,535,950; 7,499,496; 7,496,028; 7,467,338; 7,463,698; 7,443,904; 7,376,202; 7,376,074; 7,349,817; 7,345,990; 7,342,978; 7,340,006; 7,321,629; 7,315,580; 7,292,639; 7,002,904; 6,925,128; 7,535,950; 7,499,496; 7,496,028; 7,467,338; 7,443,904; 7,376,074; 7,349,817; 7,345,990; 7,342,978; 7,340,006; 7,339,884; 7,321,629; 7,315,580; 7,301,891; 7,292,639; 7,002,904; 6,925,128; 5,302,914; 20100142475; 20100124294; 20100002800; 20090303868; 20090238064; 20090147870; 20090135949; 20090110034; 20090110033; 20090097579; 20090086848; 20090080500; 20090074093; 20090067318; 20090060073; 20090060070; 20090052577; 20090052561; 20090046702; 20090034407; 20090016464; 20090011722; 20090003308; 20080310383; 20080298490; 20080285673; 20080285432; 20080267312; 20080232235; 20080112496; 20080049602; 20080008084; 20070291860; 20070223365; 20070217329; 20070189334; 20070140367; 20070121483; 20070098094; 20070092017; 20070089015; 20070076588; 20070019537; 20060268672; 20060247898; 20060245346; 20060215732; 20060126748; 20060120269; 20060120268; 20060115010; 20060098747; 20060078066; 20050270968; 20050265468; 20050238110; 20050100108; 20050089116; and 20050089109.
See, also, each of which is expressly incorporated herein by reference:    VIJAYARANGAN, ET AL., “An overview of techniques for reducing peak to average power ratio and its selection criteria for orthogonal frequency division multiplexing radio systems”, Journal of Theoretical and Applied Information Technology, vol 5, no. 5 (February 2009).    HUSSAIN, ET AL., “Tone reservation's complexity reduction using fast calculation of maximal IDFT element”, IEEE, IWCMC 08, Greece (2008)    ZHAO, ET AL., “A study on the PAPR reduction by hybrid algorithm based on the PTS and Gtechnique”, The Journal of the Korean Institute of Communication Sciences, Vol. 31, No. 2A, p. 187, February 2006.    MARSALEK, “On the reduced complexity interleaving method for OFDM PAPR reduction”, Radioengineering, vol. 1, no 3, September 2006    WU, ET AL., “8B/10B Codec for efficient PAPR reduction in OFDM communication systems”, IEEE Int'l Conf on Wireless Communications, Networking and Mobile Computing (WCNMC), Jun. 13-16, 2005, Maui, Hi., USA.    HUSSEIN, ET AL., “Performance enhancement of STBC OFDM-CDMA system using channel coding techniques over multipath fading channel”, Journal of Theoretical and Applied Information Technology, Vol. 5, No. 5, pp. 591-601, June, 2009.    MULLER, ET AL., “OFDM with reduced peak-to-average power ratio by multiple signal representation”, Annals of Telecommunications, vol. 52, no 1-2, pp. 58-67, February 1997    MOBASHER, ET AL., “Integer-based constellation shaping method for PAPR reduction in OFDM systems”, IEEE Transactions on Communications, vol. 54, pp. 119-126, January 2006.    DEUMAL, ET AL., “Peak reduction of multi-carrier systems by controlled spectral outgrowth”, Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP), 2006.    WEN, ET AL., “The PAPR reduction in OFDM system with the help of signal mapping scheme”, International Journal of Applied Science and Engineering 2007, 5, 1: 75-80    SOHN, “RBF neural network based SLM peak-to-average power ratio reduction in OFDM systems, ETRI Journal, Volume 29, Number 3, June 2007    SATHANANTHAN, ET AL., “Reducing intercarrier interference in OFDM systems by partial transmit sequence and selected mapping”, Proc. Int'l. Symp. on DSP for Comm. Systems, 2002.    TSENG, ET AL., “A reduced-complexity PTS scheme for peak-to-average power ratio reduction in OFDM systems”, Proc. European Society for Signal Processing (EURASIP) 2008.    BEHRAVAN, ET AL., “Iterative estimation and cancellation of nonlinear distortion in OFDM systems”, www.mantracom.com/downloads Jun. 19, 2008    VIJAYARANGAN, ET AL., “Reducing peak to average power ratio in orthogonal frequency division multiplexing using modified peak factor mapping”, IE(I) Journal-ET (February, 2008)    PRADABPET, ET AL., “A new PAPR reduction in OFDM systems using PTS combined with APPR for TWTA nonlinear HPA”, Songklanakarin J. Sci. Technol. 30 (3), 355-360, May-June 2008    MATEJKA, “DRM PAPR distribution and its relation to classical AM power amplifier”, www.urel.feec.vutbr.cz/ra2008/archive/ra2003/papers/169.pdf, Radioelektronika 2003    DE FIGUEIREDO, “Adaptive pre-distorters for linearization of high power amplifiers in OFDM wireless communications”, IEEE North Jersey Section CASS/EDS Chapter, Distinguished lecture    TAHA, “Performance analysis of ICC technique for OFDM PAPR reduction and its application over BTC, Master's degree project, Stockholm, Sweden 2006    JAYALATH, ET AL., “On the PAR reduction of OFDM signals using multiple signal representation”, IEEE Communications Letters, vol. 8, no. 7, July 2004    ANDGART, ET AL., “Designing Tone Reservation PAR reduction”, EURASIP Journal on applied Signal Processing, vol 2006, article ID 38237, pages 1-14    SIEGL, ET AL., “Partial transmit sequences for Peak-to-average power ratio reduction in multiantenna OFDM”, EURASIP Journal on Wireless Communications and Networking, vol. 2008, article ID 325829, 11 pages    WEN, ET AL., “A sub-optimal PTS algorithm based on particle swarm optimization technique for PAPR reduction in OFDM systems”, EURASIP J. Wireless Commun. and Networking (January 2008).    DENG, ET AL., “OFDM PAPR reduction using clipping with distortion control”, Proc. 2005 IEEE Conf. on Communications.    LIN, ET AL., “Selective-mapping type peak power reduction techniques for turbo coded OFDM”, 2005 International Conference on Wireless Networks, Communications and Mobile Computing    AL-KEBSI, ET AL., “Throughput enhancement and performance improvement of the OFDM based WLAN system”, IJCSNS International Journal of Computer Science and Network Security, vol. 9, no. 4, April 2009    GIANNOPOULOS, ET AL., “Novel efficient weighting factors for PTS-based PAPR reduction in low-power OFDM transmitters”,www.eurasip.org/proceedings/Eusipco/Eusipco2006/papers/1568982220 2006    WULICH, ET AL., “Is PAPR reduction always justified for OFDM?”, Proc. European Wireless Conference, 2007.    WESOLOWSKI, “On the PAPR minimization using selected mapping algorithm in pilot-assisted OFDM systems”, Proc. European Wireless Conference, 2007.    ALHARBI, ET AL., “A combined SLM and closed-loop QO-STBC for PAPR mitigation in MIMO-OFDM transmission”. www.eurasip.org/proceedings/Eusipco/Eusipco2008/papers/1569102063 2008    YANG, ET AL., “Selective vector perturbation precoding and peak to average power ratio reduction of OFDM systems”, Proc. IEEE Global Telecommunications Conf., 2008.    TSAI, ET AL., “A tail-biting turbo coded OFDM system for PAPR and BER reduction”, 2007 IEEE Vehicular Technology Conference.    BAXLEY, “Analyzing selected mapping for peak-to-average power reduction in OFDM”, Thesis, School of Electrical and Computer Engineering, Georgia Institute of Technology, May 2005    WANG, “Peak to average power ratio reduction for OFDM”, Research & Standards LGE Mobile Research, USA, Aug. 27, 2007, 3GPP2, TSG-C NTAH.    PARK, ET AL., “Tone reservation method for PAPR reduction scheme”, IEEE 802.16e-03/60    BREILING, ET AL., “SLM peak-power reduction without explicit side information”, IEEE Communications Letters, vol. 5, no. 6, June 2001    GUEL, ET AL., “Approximation of the average power variation for geometric adding signal approach of PAPR reduction in context of OFDM signals”, Union Radio Scientifique Internationale-URSI, Aug. 7-16, 2008, Chicago, Ill.    HUSSAIN, ET AL., “Peak to average power ratio reduction for multi-band OFDM system using tone reservation”, www.ursi-test.intec.ugent.be/files/URSIGA08/papers/CPS2p5 2008    VALBONESI, ET AL., “Low-complexity method for PAPR reduction in OFDM based on frame expansion parameter selection”, 13th European Signal Processing Conference, Sep. 4-8, 2005, Antalya, Turkey    BREILING, ET AL., “Distortionless reduction of peak power without explicit side information”, 2000 IEEE Global Telecommunications Conference.    JAYALATH, ET AL., “Use of data permutation to reduce the peak-to-average power ratio of an OFDM signal”, Wireless Communications and Mobile Computing, 2002, 2:187-203    JAYALATH, ET AL., “On the PAR reduction of OFDM signals using multiple signal representation”, IEEE communications Letters, vol. 8, no. 7, July 2004    JAYALATH, ET AL., “SLM and PTS peak-power reduction of OFDM signals without side information”, IEEE Trans. on Wireless Communications, vol. 4, no. 5, September 2005    VEERAGANDHAM, “Orthogonal frequency division multiplexing” EECS 865:Wireless Communications    FISCHER, ET AL., “Directed selected mapping for peak-to-average power ratio reduction in MIMO OFDM”, Proc. International OFDM Workshop, 2007.    FISCHER, “Widely-linear selected mapping for peak-to-average power ratio reduction in OFDM”, Electronics Letters, vol. 43, 2007.    WANG, “Reduction of the PAPR in OFDM signals by applying PTS mechanism”, Master Thesis, Institute of Communication Engineering, Tatung University, January 2004    LIN, “Performance analysis in the PAPR of OFDM system via SLM scheme”, Master Thesis, Institute of Communication Engineering, Tatung University, January 2004    RAJBANSHI, ET AL., “Peak-to-average power ratio analysis for NC-OFDM transmissions”, Proc. 2007 IEEE Vehicular Technology Conference.    SAITO, ET AL., “PAPR reduction of MC-CDMA signals by selected mapping with interleavers”, Multi-Carrier Spread-Spectrum, Springer Netherlands, pp. 453-460    HABENDORF, ET AL., “Nonlinear predistortion with reduced peak-to-average power ratio”, Proc. International Symposium on Wireless Communications.    HOSSEINI, ET AL., “PAPR reduction in OFDM systems using polynomial-based compressing and iterative expanding”, 2006 IEEE ICASSP.    FISCHER, ET AL., “Peak-to-average power ratio reduction in MIMO OFDM”, Proc. 2007 Int. Conf on Communications, pp. 762-767.    RAGUSA, ET AL., “Invertible clipping for increasing the power efficiency of OFDM amplification”, Proc. 2007 IEEE Int. Symposium on Personal Indoor and Mobile Radio Communications.    SEZGINER, ET AL., “Metric-based symbol predistortion techniques for peak power reduction in OFDM systems”, IEEE Trans. on Wireless Communications, vol. 6, no. 7, July 2007    SIEGL, ET AL., “Peak-to-average power ratio reduction in multi-user OFDM”, Proc. 2007 IEEE Int. Symp. on Information Theory.    HENKEL, ET AL., “Partial transmit sequences and trellis shaping”, Proc. 5th Int. ITC Conf. on Source and Channel Coding, 2004.    LEE, ET AL., “Unitary peak power reduction for short packet communications in multiple transmit antennas”, IEEE Trans. Commun., vol. 56, February 2008, pp. 234-244.    LOYKA, ET AL., “On the peak factor of sampled and continuous signals”, Proc. 2006 IEEE Vehicular Technology Conf.    LIN, ET AL., “Selective-mapping type peak power reduction techniques for turbo coded OFDM”, 2005 IEEE Conf. on Wireless Networks, Communications and Mobile Computing.    BONACCORSO, ET AL., “Reducing the peak to average power ratio in OFDM systems”, Dix-septieme colloqueGRETSI, Vannes, 13-17 September 1999    BAXLEY, ET AL., “Assessing peak-to-average power ratios for communications applications”, Proc. IEEE Military Communications Conf (MILCOM 2004).    CHEN, ET AL., “A modified selective mapping with PAPR reduction and error correction in OFDM systems”, 2007 IEEE Wireless Com. and Networking Conf., pp. 1329-1333.    FISCHER, “Peak-to-average power ratio (PAR) reduction in OFDM based on lattice decoding”, Proc. Int. OFDM Workshop.    SIEGL, ET AL., “Directed selected mapping for peak-to-average power ratio reduction in single-antenna OFDM”, Proc. Int. OFDM Workshop.    CIOCHINA, ET AL., “An analysis of OFDM peak power reduction techniques for WiMAX systems’, Proc. 2006 Int. Conf on Communications, pp. 4676-4681.    MALKIN, ET AL., “Dynamic allocation of reserved tones for PAR reduction”, OFDM Workshop, August 2008, Hamburg Germany    PRADABPET, ET AL., “A new PTS method using GA for PAPR reduction in OFDM-WLAN 802.11a systems”, www.jcsse.org/slide/comp_int/P0014.pdf    WU, ET AL., “Peak-to-average power ratio reduction in OFDM based on transformation of partial transmit sequences”, Electronics Letters, Jan. 19, 2006, vol. 42, no. 2    HAIDER, “Peak to average ratio reduction in wireless OFDM communication systems”, Thesis, Blekinge Institute of Technology, January 2006    HENKEL, ET AL., “Another application for trellis shaping: PAR reduction for DMT (OFDM), IEEE Transactions on Communications, vol. 48, no. 9, September 2000    FISCHER, ET AL., “Peak-to-average power ratio reduction in single- and multi-antenna OFDM via directed selected mapping”, Jul. 19, 2007    HERRAIZ, “Multicarrier communication systems with low sensitivity to nonlinear amplification”, Thesis, Eng. i Arquitectura La Salle, Univers. Ramon Llull, Barcelona 2008    KASIRI, ET AL., “A preprocessing method for PAPR reduction in OFDM systems by modifying FFT and IFFT matrices”, The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'07)    MALKIN, ET AL., “Optimal constellation distortion for PAR reduction in OFDM systems”, Proc. 2008 PIMRC.    WEI, ET AL., “A modern extreme value theory approach to calculating the distribution of the peak-to-average power ratio in OFDM systems”, 2002 IEEE Int. Conf. on Communications, vol. 3, pp. 1686-1690.    RAJBANSHI, ET AL., “Adaptive-mode peak-to-average power ratio reduction algorithm for OFDM-based cognitive radio”, 2006 IEEE Vehicular Technology Conf.    REN, “An improved selected mapping scheme for PAPR reduction in OFDM systems”, Thesis, University of Cincinnati    SOHN, “RBF neural network based SLM peak-to-average power ratio reduction in OFDM systems, ETRI Journal, vol. 29, no. 3, June 2007    BOONSRIMUANG, ET AL., “Mitigation of non-linear distortion using PTS and IDAR method for multi-level QAM-OFDM system”, ECTI Transactions on Computer and Information Technology, vol. 1, no. 2, November 2005.    SCHENK, ET AL., “The application of spatial shifting for peak-to-average power ratio reduction in MIMO OFDM systems”, Proc. 2006 IEEE Vehicular Technol. Conf.    SCHENK, ET AL., “Peak-to-average power reduction in space division multiplexing based OFDM systems through spatial shifting”, Electronics Letters, Jul. 21, 2005, vol. 41, no. 15    NAWAZ, ET AL., “PAPR reduction technique for OFDM systems with rotated MPSK constellations and coordinate interleaving”, Proc. 2008 IEEE Symp on Comm. & Veh. Technol.    VAN WELDEN, ET AL., “Clipping versus symbol switching for PAPR reduction in coded OFDM”, 15th Annual Symposium of the IEEE/CVT Benelux Chapter, Nov. 13, 2008    SHARIF, ET AL., “On the peak-to-average power of OFDM signals based on oversampling”, IEEE Transactions on Communications, vol. 51, no. 1, January 2003    BAXLEY, ET AL., “Ordered phase sequence testing in SLM for improved blind detection”, Proc. 2005 IEEE Conf on Signal Processing Advances in Wireless Communication.    SCHURGERS, ET AL., “A systematic approach to peak-to-average power ratio in OFDM”, Proc. SPIE vol 4474, p. 454 (2001).    FISCHER, ET AL., “Signal shaping for peak-power and dynamics reduction in transmission schemes employing precoding”, IEEE Trans. on Comm., v50, pp. 735-741, 5/2002.    JIANG, ET AL., “Two novel nonlinear companding schemes with iterative receiver to reduce PAPR in multi-carrier modulation systems”, IEEE Transaction on Broadcasting, vol. 52, pp. 268-273, June 2006.    JAFARI, “Adaptive lattice reduction in MIMO systems”, Thesis, University of Waterloo, Canada, 2008    PISE, ET AL., “Packet forwarding with multiprotocol label switching” World Academy of Science, Engineering and Technology 12 2005    BOCCARDI, ET AL., “The p-sphere encoder: vector precoding with low peak-power for the MIMO Gaussian Broadcast Channel”, IEEE Trans. Comm., vol. 54, p. 1703, September 2006.    DEVLIN, ET AL., “Gaussian pulse based tone reservation for reducing PAPR of OFDM signals”, 2007 IEEE Vehicular Technol. Conf.    RAJBANSHI, ET AL., “OFDM symbol design for peak-to-average power ratio reduction employing non-data bearing subcarriers”, Proc. 2008 IEEE Wireless Communications and Networking Conference, pp. 554-558.    ZHAO, “Distortion-based crest factor reduction algorithms in multi-carrier transmission systems”, A Dissertation, Georgia Institute of Technology, December 2007    RAJBANSHI, “OFDM-based cognitive radio for DSA networks”, Technical Report, The University of Kansas (2007).    SARI, “OFDM peak power reduction techniques performance analysis for WiMAX Systems” Sequans Communications, 4th Annual Wireless Broadband Forum (2005).    Lee et al., “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems”, Proc. 2008 IEEE Global Telecommunications Conf GLOBECOM 2008.    Jimenez et al., “Study and Implementation of complementary Golay sequences for PAR reduction in OFDM signals”, Proc. 11th Med. Electrotech. Conf. MELECON 2002, pp. 198-203.    CHOI, ET AL., “Peak power reduction scheme based on subcarrier scrambling for MC-CDMA systems”, IEE Proceedings on Communications, vol. 151, pp. 39-43, February 2004.    “Peak-to-average power ratio (PAPR)”, Wireless Inf. Trans. System Lab., Mar. 2, 2006    WANG, “PAPR reduction for OFDM”, circa 2007.    GIANNOPOULOS, ET AL., “Relationship among BER, power consumption and PAPR”, 2008 IEEE Int. Symp on Wireless Pervasive Computing, pp. 633-637.    INDERJEET KAUR, et al., “The Minimum PAPR Code for OFDM Systems”, World Academy of Science, Engineering and Technology 46 2008 p. 285.    O. DAOUD, et al., “PAPR Reduction by Linear Coding Techniques for MIMO-OFDM Systems Performance Improvement: Simulation and Hardware Implementation”, European Journal of Scientific Research, Vol. 36 No. 3 (2009), pp 376-393.    Ting-Jung Liang et al., “Synchronization in OFDM-based WLAN with Transmit and Receive Diversities”, in IEEE 16th Intl. Symp. on Personal, Indoor and Mobile Radio Comm., PIMRC 2005., vol. 2, 11-14 Sep. 2005, pp. 740-744.